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Basics of signal processing, design of specimens, system acquisition
Basic of Sensor and Transducers
Dr. Simone Peloso
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General principles
Meaningful interpretation of the model tests is not possible unless proper instrumentation is used for measuring the many important quantities related to the behaviour of the structure.
The instrumentation process includes:
• Careful identification of the quantities to be measured;
• Selection of the appropriate sensors and the auxiliary equipment;
• Installation of the sensors on the completed model;
• Calibration of sensors;
• Checkout of equipment prior to the model test;
• Acquisition of data;
• Reduction of data into meaningful stresses, forces, and force–deformation relationships.
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General principles
The behaviour of a structure is reflected in the forces and deformations that result from subjecting it to the different loading conditions.
In general the following quantities need measurement:
1. Strain: Strain may be measured in concrete, either by instrumenting the surface or by suitably embedding gages inside, or on the steel reinforcement and the prestressing strands.
2. Deflection: Its distribution along the structure and its variation with the applied load and magnitude in a structure or a constituent element. (Deflection measurements are needed to define the load–deformation characteristics and can be helpful in determining the limits of elastic behavior, curvature, and changes in curvature.)
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Quantities to be measured
3. Cracks: Their locations, patterns, and widths related to the loading. (This information is used to determine satisfactory service load conditions and also to obtain the ultimate or limit load stress conditions.)
4. Forces: Their magnitudes and nature in the concrete or the steel reinforcement, at the boundary supports, and sometimes at loading points. (Knowledge of these internal forces, which are in equilibrium with the applied forces is especially useful in the study of indeterminate structures.)
5. Temperature: Its distribution within the mass of concrete, where the structure is subjected to differential temperature conditions.
6. Creep and shrinkage: Their measurements in a structure subjected to sustained
loading. (These are similar to item 1 above, but care must be exercised to ensure that the instrumentation is stable over the entire period of measurement.
7. Properties of materials: They must be determined in order to translate other measurements (such as strains) into overall structural behaviour, and to correlate test results with theory. (Measurement of properties of concrete are particularly important since they are subject to variations from environmental conditions, such as relative humidity and temperature.)
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Quantities to be measured
8. Dynamic response: Various types of responses of a structure when subjected to dynamic loads (e.g. impact, blast, seismic, fatigue and repeated loadings). Accelerations, velocities, and displacements are measured.
NOTES:
• The equipment to measure the above quantities varies from simple hand instruments to the more‐sophisticated electronic devices.
• The readout instruments accompanying these measuring devices also vary from hand‐operated to continuous scanning, recording, and monitoring systems
• The outcome of any experimental program depends significantly on the accuracy and reliability of measurements. (In the case of small‐scale models, the quantities to be measured are much smaller in magnitude, based on the principles of similitude thus magnifying the error possibility and the associated need for accuracy)
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Perofrmance specification
Proper selection and integration of sensors and transducers are crucial in “instrumenting” a vibrating system.
A measuring device passes through two stages in making a measurement.
Sensor stage
Transducer stage
It is common practice to identify the combined sensor– transducer unit as either
a sensor or a transducer
The measurand is sensed
The measured signal is transduced(i.e. converted) into an electrical signal
Signal conditioning, Processing, or Recording
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Performance specification
In most applications, the following variables are particularly useful in determining the response and structural integrity of a vibrating system
Strain gaugeStress and Strain
AccelerometerAcceleration
Tachometer or GeophonesVelocity
Potentiometer or LVDTDisplacement
Measuring DevicesResponse Variable
Transducers are divided into two broad categories:
Passive transducers do not require an external electric source for activation: electromagnetic, piezoelectric and photovoltaic transducers
Active transducers do not possess self‐contained energy sources and thus need external activation: resistive transducers such as potentiometers
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Performance specification
In most applications, the following variables are particularly useful in determining the response and structural integrity of a vibrating system
Strain gaugeStress and Strain
AccelerometerAcceleration
Tachometer or GeophonesVelocity
Potentiometer or LVDTDisplacement
Measuring DevicesResponse Variable
Transducers are divided into two broad categories:
Passive transducers do not require an external electric source for activation: electromagnetic, piezoelectric and photovoltaic transducers
Active transducers do not possess self‐contained energy sources and thus need external activation: resistive transducers such as potentiometers
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Transducers
Generally speaking, a transducer is a device that converts one type of energy to another.
Transducers are the input element in a measurement system.
The transducer is the device sensing the physical quantity that is to be measured and producing an electrical output.
A transducer may contain one or more sensors which transmit a signal to a measurement unit producing the electrical output.
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Accuracy and Precision
The measurement accuracy determines the closeness of the measured value to the true value.
The precision of an instrument is determined by the standard deviation of error in the instrument response.
%)(TrueValue
)(TrueValuealue)(MeasuredVorErr
The measurement error may be represented by a random variable using its mean value and its standard deviation
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Sensitivity and Resolution
The sensitivity of a transducer is defined as
The sensitivity may be computed from the input‐output relationship as the derivative dy/dx.
When the relationship is linear, the sensitivity is the angular coefficient of the straight line a.
The resolution of a sensor is the smallest change it can detect in the quantity that it is measuring.
quantityphysicalinchange
quantityelectricalinchangeysensitivit
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Input‐Output relationship
In static conditions, the behaviour of a transducer may be described by different parameters that can be deduced from the input‐output relationship of the device.
The transducer is linear if its input‐output relationship may be described by a straight line, i.e. in the form y=ax+b
ΔX
∆Y
Electric quantity
[EQ]
(output)
Physical quantity[PQ]
(input)
IO relationship
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Threshold and Range
The threshold is the minimum input value for the physical quantity to produce a non zero output of the transducer.
The range is the interval of the physical quantity’s values that the transducer is able to measure, defined by its inferior and superior limits.
EQ(output)
PQ
(input)
Threshold
Threshold
Range
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Hysteresis and Errors
Hysteresis is the maximum difference between the increase and decrease paths of the transducer output during a cycle extending to the range limits.
A load curve and an unload curve must be used to infer the proper measurement.
e.q.
p.q.
e.q.
p.q.
The error of a transducer is the difference between the real and the ideal transducer behavior.
The error band is the area around the input‐output curve that covers the worse measurement error.
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Dynamic behavior
When the physical quantities to be measured may vary rapidly in time, as in the case of dynamic tests, one needs to ensure that the transducers may be able to follow its changes without altering the measurement.
This may be accomplished by studying the sensitivity of the transducer as a function of frequency, i.e. the bode diagram of the transfer function of the transducer.
-25
-20
-15
-10
-5
0
5
Ma
gnitu
de
(d
B)
10-1 100 101 102 103-90
-45
0
45
Pha
se (
deg)
Bode Diagram
Frequency (rad/sec)
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Instrument ratings
In selecting a particular transducer (measuring device) for a specific vibration application, special attention should be give to its ratings, which usually are provided by the manufacturer, and the required performance specifications as provided by the customer (or developed by the system designer).
Typical rating parameters supplied by instrument manufacturers are:
Sensitivity of a transducer is measured by the magnitude (peak, root‐mean‐square [RMS] value, etc.) of the output signals corresponding to a unit input of the measurand. This may be expressed as the ratio of (incremental output)/(incremental input) or, analytically, as the corresponding partial derivative. In the case of vectorial or tensorial signals (e.g., displacement, velocity, acceleration, strain, force), the direction of sensitivity should be specified.
Cross‐sensitivity is the sensitivity along directions that are orthogonal to the direction of primary sensitivity; it is expressed as a percentage of the direct sensitivity. High sensitivity and low cross sensitivity are desirable for measuring instruments. Sensitivity to parameter changes, disturbances, and noise has to be small in any device, however; this is an indication of its robustness. Often, sensitivity and robustness are conflicting requirements
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Instrument ratings
Dynamic range of an instrument is determined by the allowed lower and upper limits of its input or output (response) so as to maintain a required level of measurement accuracy. This range is usually expressed as a ratio, in decibels. In many situations, the lower limit of the dynamic range is equal to the resolution of the device. Hence, the dynamic range is usually expressed as the ratio (range of operation)/(resolution), in decibels.
Linearity is determined by the calibration curve of an instrument. The curve of output amplitude vs. input amplitude under static conditions within the dynamic range of an instrument is known as the static calibration curve. Its closeness to a straight line measures the degree of linearity. Manufacturers provide this information either as the maximum deviation of the calibration curve from the least squares straight‐line fit of the calibration curve or from some other reference straight line. If the least squares fit is used as the reference straight line, the maximum deviation is called independent nonlinearity, Nonlinearity may be expressed as a percentage of either the actual reading at an operating point or the full‐scale reading.
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Instrument ratings
Zero drift is defined as the drift from the null reading of the instrument when the measurand is maintained steady for a long period. Note that in this case, the measurand is kept at zero or any other level that corresponds to null reading of the instrument.
Usual causes of drift include:
• instrument instability
• ambient changes (e.g., changes in temperature, pressure, humidity, and vibration level)
• changes in power supply (e.g., changes in reference DC voltage or AC line voltage),
• parameter changes in an instrument (due to aging, nonlinearities, etc.).
Bandwidth of an instrument determines the maximum speed or frequency at which the instrument is capable of operating. High bandwidth implies faster speed of response. Bandwidth is determined by the dominant natural frequency of the transducer. Instrument bandwidth must be several times greater than the maximum frequency of interest in the measured signal. The bandwidth of a measuring device is important, particularly when measuring transient signals. Note that the bandwidth is directly related to the useful frequency range.
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Instrument ratings
Useful frequency rangecorresponds to the interval of both flat gain and zero phase in the frequency response characteristics of an instrument. The maximum frequency in this band is typically less than half the dominant resonant frequency of the instrument.
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-20
-15
-10
-5
0
5
Ma
gnitu
de
(d
B)
10-1 100 101 102 103-90
-45
0
45
Pha
se (
deg)
Bode Diagram
Frequency (rad/sec)
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Instrument ratings
Examples of rating parameters of several sensors and transducers
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Linear position transducers
Linear potentiometers are devices allowing to transduce linear displacements.
They have three connectors: ground, Vcc
(supply) and V (output connector).
Resistance‐based potentiometers may use a wire winding around cylindrical core or a thin carbon layer as resistors.
The output connector may translate and is rigidly attached to the object whose displacement we want to measure. The displacement of the object of interest therefore causes a displacement of the cursor on the resistor (X), which causes a change in the output voltage of the pot.
L
X
V
E
XL
VE
=
X E
VL
If the resistance has uniform resistivity
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Wire vs Carbon
A common drawback of the wrapped wire potentiometer is the resulting discrete resolution of its input‐output relationship: each wrapping (coil) produces a step in the output function.
The life span of these transducers is limited by the wearing of the resistance due to mechanical friction.
The force necessary to overcome the friction of the cursor alters the measurement.
A conditioning circuit to filter out the high frequency noise related to cursor displacement is usually necessary
V
X
Potentiometers based on a carbon film overcome the resolution limitation of wired pots, yet they tend to be less linear and wear down faster.
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Linear Variable Differential Transformer (LVDT)
The operation of the LVTD is based on the principle of variable mutual inductance.
The transducer consists of one primary coil and two secondary coils which are coupled through a moving core whose position is tied to the displacement to be measured.
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Linear Variable Differential Transformer (LVDT)
An alternating current is driven through the primary, causing a voltage to be induced in each secondary proportional to its mutual inductance with the primary.
As the core moves, these mutual inductances change, causing the voltages induced in the two secondary to change.
The coils are connected in reverse series, so that the output voltage is the difference between the two secondary voltages.
2
L~
E1
E X
V=E1 -E2
E2
2
L
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When the core is in its central position equal but opposite voltages are induced in the two secondary coils and the output voltage is zero.
When the core is displaced in one direction, the voltage in one coil increases as the other decreases, causing the output voltage to increase from zero to a maximum, corresponding to the flux concatenating only the first coil.
Linear Variable Differential Transformer (LVDT)
The magnitude of the output voltage is proportional to the distance moved by the core, making it a linear transducer.
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When the core is displaced in one direction, the voltage in one coil increases as the other decreases, causing the output voltage to increase from zero to a maximum, corresponding to the flux concatenating only the first coil.
This voltage is in phase with the primary voltage.
When the core moves in the other direction, the opposite occurs and the phase of the output voltage is opposite to that of the primary.
Linear Variable Differential Transformer (LVDT)
The phase of the voltage indicates the direction of the displacement.
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LVDT principles
The magnetic flux for each coil facing the core will be
Thus if N1 and N2 are the coils facing the core, the flux concatenating with the secondary windings becomes:
Thus the electromotive force induced in each secondary is:
And therefore the differential output voltage will be:
Considering that n indicates the number of coils per unit displacement in the two secondary windings, the output voltage is related to the core displacement X by:
BS
1 1
2 2
( )
( )
N X
N X
E j
E j1 1
2 2
=
=
2V j nX
1 2 1 2 V E E j N X N X
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The secondary output signal is then processed by a phase‐sensitive demodulator which is switched at the same frequency as the primary energy supply.
This results in a final output which, after rectification and filtering, gives D.C. output proportional to the core movement and also indicates its direction, positive or negative from the central zero point.
Because the sliding core does not touch the inside of the tube, it can move without friction, making the LVDT a highly reliable device.
The absence of any sliding or rotating contacts allows the LVDT to be completely sealed against the environment.
Linear Variable Differential Transformer (LVDT)
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LVDTs are commonly used for position feedback in servomechanisms, and for automated measurement in machine tools and many other industrial and scientific applications.
Linear Variable Differential Transformer (LVDT)
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Instruments: Objectives
Measurement of the quantities of interest:
Local information:• Element curvatures in the critical
sections• Steel strain across the plastic hinges
Damage related quantities:• Floor displacements and rotations• Interstorey drifts• Shear deformation of infill panels
Global quantities:• Floor accelerations (dynamic
amplification of motion)• Proportions between the accelerations
at different points across the structure (dynamic identification)
Deformations
Displacements
Accelerations
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Instruments: Objectives
Measurement of the quantities of interest:
Direct Measure:• Strain Gauges
Deformations
• Video acquisition with High Definition Cameras
Displacements
• AccelerometerAccelerations
Derived Measure:• Rectilinear Displacement Transducers
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Instruments
Rectilinear Displacement Transducers
Direct measure:•Relative displacements between the two ends of the instruments.
Derived measure:•Average deformation along the instrument length;•Average curvature (with more than one instrument)
Useful stroke from 25 to 250 mm
Infinite resolution
Displacement speed up to 10 m/s
Displacement force < 0.5 N
Electric output 010 V
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Instruments
Rectilinear Displacement Transducers
Derived measure:
Average deformation
Average curvature
1 2
L
L1
1
L2
2
h21
h
1 2
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Instruments
Rectilinear Displacement Transducers
Derived measure:
Shear deformation of infill panels
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Accelerometers
An accelerometer is a transducer measuring proper acceleration (i.e. relative to free fall, or an inertial frame).
The most common accelerometer consists in a box containing a known mass which can move on a linear path and is held by a spring attached to the box.
The mass is also attached to a damper, introducing a viscous term in the equilibrium equation and reducing the oscillations which would result from step displacements.
The displacement of the mass is then transduced by a linear potentiometer (friction less).
0 xKxD)sx(M
s
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Mass Spring Damper Accelerometer
When the accelerometer experiences an acceleration, the mass is displaced to the point that the spring is able to accelerate the mass at the same rate as the casing. The displacement is then measured to give the acceleration.
0 sxKsxsDMasxMs2
saMsxKsxsDsxMs2
MKsMDs
1
sa
sx2
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Frequency response
The dynamic response of the mass‐spring‐damper accelerometer typically resembles the one shown in figure.
At low frequencies,
the relationship X = - M/K a holds,
while at relatively high frequencies there is a peak of resonance followed by a rapid gain decrease.
The applicability of these transducers therefore ranges between 0 rad/s and the resonance frequency ωres
log Xa
log
/res K M
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MEMS accelerometers
Modern accelerometers take advantage of current manufacturing technologies allowing the miniaturization of devices and their implementation as micro electro‐mechanical systems (MEMS).
These often measure the deflection of a heated gas bubble from the center of the device.
The square in the middle of the chip is a resistor that heats up a gas bubble. As the device is moved, surrounding thermal couples sense the location of the bubble.
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MEMS accelerometers
Modern accelerometers take advantage of current manufacturing technologies allowing the miniaturization of devices and their implementation as micro electro‐mechanical systems (MEMS).
Most MEMS work in‐plane: they are designed to be sensitive only to a one or two directions in the plane of the circuit. By adding an additional out‐of‐plane device three axes can be measured.
This solution always has a much lower misalignment error than three discrete devices combined.
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Typical MEMS accelerometers exhibit a ±1 g to ±10 g range.
Sensitivity is often ratiometric (i.e. the output of the instrument is directly proportional to the input), for a 5 V power supply these may be 25 to 500 mV/g, depending on the range of the device.
Manufacturers:
‐ Analog Devices;
‐ ST microelectronics;
‐Memsic;
‐ …
MEMS accelerometers
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A piezoelectric accelerometer that utilizes the piezoelectric effect of certain materials to measure accelerations.
As with all transducers, piezoelectric accelerometers convert one form of energy into another, specifically they provide an electrical signal in response to the acceleration being measured.
Piezoelectric accelerometers
Piezoelectric materials used for the purpose of accelerometers can also fall into two categories.
The first, and more widely used, is single‐crystal materials (usually quartz). PRO: long life span in terms of sensitivity;
CON: less sensitive than some piezoelectric ceramic.
The second is piezoelectric ceramic materials.
PRO: higher piezoelectric constant (sensitivity); lower production costs;
CON: their sensitivity degrades with time (shorter life span)
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Using the general sensing method upon which all accelerometers are based, acceleration acts upon a seismic mass that is restrained by a spring or suspended on a cantilever beam, and converts a physical force into an electrical signal.
Before the acceleration can be converted into an electrical quantity it must first be converted into either a force or displacement. This conversion is done via the mass spring system shown in the figure.
Piezoelectric accelerometers
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The seismic mass and the piezoceramics (plus other "flexible" components) form a spring mass system. It shows the typical resonance behavior and defines the upper frequency limit of an accelerometer. In order to achieve a wider operating frequency range the resonance frequency should be increased. This is usually done by reducing the seismic mass. However, the lower the seismic mass, the lower the sensitivity. Therefore, an accelerometer with high resonance frequency, for example a shock accelerometer, will be less sensitive whereas a seismic accelerometer with high sensitivity has a low resonance frequency.
Piezoelectric accelerometers
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Figure shows a typical frequency response curve of an accelerometer when it is excited by a constant acceleration. Several useful frequency ranges can be derived from this curve:
Piezoelectric accelerometers
At approximately 1/5 the resonance frequency (0.2 fr) the response of the sensor is 1.05. This means that the measured error compared to lower frequencies is 5 %.
At approximately 1/3 the resonance frequency (0.3 fr) the error is 10 %. For this reason the "linear" frequency range should be considered limited to 1/3 the resonance frequency.
The 3 dB limit with approximately 30 % error is obtained at approximately one half times the resonance frequency.
Log of freq.
Error
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Figure shows a typical frequency response curve of an accelerometer when it is excited by a constant acceleration. Several useful frequency ranges can be derived from this curve:
Piezo‐electric accelerometers
The lower frequency limit mainly depends on the chosen preamplifier. Often it can be adjusted. With voltage amplifiers, the low frequency limit is a function of the RC time constant formed by accelerometer, cable, and amplifier input capacitance together with the amplifier input resistance.
Log of freq.
Error
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Positioning example
Accelerometers
Direct measure:
•Single axis acceleration
Derived measure:
•Floor acceleration
•Floor displacement and rotation
•Modal quantities
Acceleration range: 2.5 g
Resolution: 0.8 g @ < 1Hz
Resonant frequency: 5000 Hz
Weight 28 grams
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Positioning example
Accelerometers
Direct measure:
•Single axis acceleration
Derived measure:
•Floor acceleration
•Floor displacement and rotation
•Modal quantities
Acceleration range: 2.5 g
Resolution: 0.8 g @ < 1Hz
Resonant frequency: 5000 Hz
Weight 28 grams
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Strain gauge
A strain gauge is a device that measures the strain of an object by measuring the resulting deformation.
The most common type of strain gauge consists of an insulating flexible backing which supports a metallic foil pattern. In a typical strain gauge, a long, thin conductive strip is arranged in a zig‐zagpattern of lines parallel to the direction of the measurement.
The gauge is attached to the object by a suitable adhesive. As the object is deformed, the foil is deformed, causing its electrical resistance to change. This resistance change, usually measured using a Wheatstone bridge, is related to the strain by a quantity known as the gauge factor.
L
25
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Strain gauge
A strain gauge is based on the property that electrical conductance (G=1/R) does not depend only on the conductivity of a conductor (a property of its material), but it depends also on its geometry.
When an electrical conductor is stretched it will become narrower and longer, thus increasing its electrical resistance end‐to‐end.
Conversely, when a conductor is compressed it will broaden and shorten, changes that decrease its electrical resistance end‐to‐end.
From the measured electrical resistance of the strain gauge, the amount of strain may be inferred and eventually the stress can be derived.
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Gauge factor
The gauge is attached to the object with adhesive and, as the object is deformed, the gauge is deformed causing a change of its conductance. The sensitivity of the device is measured by the gauge factor:
Recall that the resistance of a conductor is related to its physical properties by
Differentiating, the gage factor may be expressed as
Where 0<α<1
Typical g values for metallic gauges is above 2. For nickel‐copper alloys it is 2, nickel‐iron‐chrome reaches 3.5 and pure nickel slightly above 12.
Higher g values may be obtained using superconductor materials, but their un‐deformed resistance is then temperature dependent.
RRg
LL
LR
S
1d
dLL
g
26
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Strain gauge circuits
To compensate for the temperature influence on the resting resistance two identical strain gauges orthogonal to each other and connected as one leg of a Wheatstone bridge.
For two dimensional measurements, four strain gauges are typically used together building a full Wheatstone Bridge
Strain is defined as
and is therefore unit less
RC RD 4A
U
V LV g
L
L
L
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Applications
Strain gauges are the building component of other types of transducers for measuring forces (if applied to a test material of known properties), torques (using a pair of strain gauges measuring the torsional deformation of a rod) and pressures.
2AV L
V gL
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Strain gauges come in a variety of sizes and shapes.
Linear displacement transducers based on strain gages typically have a full measurement range between 5 and 100 mm. Typical crack detection gauges range 10 mm to 50 mm in strand length.
Strain measures are usually very small and are usually expressed in με.
Measuring strain requires accurate measurement of very small changes in resistance. For example, suppose a test specimen undergoes a substantial strain of 500 με. A strain gauge with a gauge factor g = 2 will exhibit a change in electrical resistance of only 2∙(500 ´ 10–6) = 0.1%. For a 200 Ω resistance the change will be only 2 Ω
Strain gauge
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Positioning example
Strain Gauges
Direct measure:
•Deformation of steel bars across the plastic hinges
Note: the strain gauge has to be applied to the steel bar PRIOR to the concrete casting.
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Seismometer
The seismometer is the transducer of ground movements and is used to record seismic waves during earthquakes. The seismograph additionally includes a recording device. Seismometers may record ground displacement, velocity or acceleration vs. time.
The working principle of the traditional seismometer is similar to that of the mass‐spring accelerometer: a mass is free to move with respect to its casing while held to it by a spring‐damper system. When the ground moves, the mass tends to remain motionless in space while the frame moves with the ground. The movement of the internal mass relative to the frame is measured.
A replica of an ancient Chinese Siesmographfrom Eastern Han Dynasty (25‐220 CE)
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Seismometer
Geophones use a magnetic mass moving within a wire coil, producing an electrical signal which is proportional to ground velocity. Their frequency response is that of a harmonic oscillator, with corner frequency typically around 10Hz.
/res K M
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Teleseismometers
Modern broadband seismometers allow the measurement of movements at frequencies between close to 0.001 Hz to 30 Hz. These instruments use a negative feedback loop to hold the mass still in space with respect to the frame using an electromagnetic field. The force used to hold the mass steady is measured and ground acceleration is inferred. Devices may be multiple axis by using separate masses. Movements of the internal mass is measured using a LVDT and represent the error which thenegative feedback control loop attempts to drive to zero by varying the current driving the electromagnetic field. The latter is a precise measurement of the force needed to hold the mass steady and its acceleration can therefore be inferred as a=F/m.Data may be digitally recorded using an A/D converter and stored or periodically transmitted automatically.Special care must be used for long term monitoring instruments being exposed to large temperature excursions and weather agents.
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Force Measurement
Various types of instrumentation are available for directly measuring different forces, such as compression or tension.
‐ Load cells: for measuring reactions and external forces (strain gauge load cells are the most common)
‐ Embedded stress plugs or meters: for measuring stresses and strains inside a concrete structure
‐ Stress sensitive paints: between washers to measure forces by the electrical resistance of these paints
Although most of these are available commercially, often their use is precluded because of economic factors and the nature of the experiment; e.g., a load cell required for measuring reactions in a small‐scale beam test may not be available in that small size or else may not fit in the available space for the measurement. In such a case, laboratory available equipment can be easily used to fabricate the required load cell.
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Load cells
A load cell is an electronic device (transducer) that is used to convert a force into an electrical signal.
This conversion is indirect and happens in two stages:
1) Through a mechanical arrangement, the force being sensed deforms a strain gauge.
2) The strain gauge converts the deformation (strain) to electrical signals.
A load cell usually consists of four strain gauges in a Wheatstone bridgeconfiguration.
The electrical signal output is typically in the order of a few millivolts and requires amplification by an instrumentation amplifier before it can be used.
The output of the transducer is plugged into an algorithm to calculate the force applied to the transducer
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Load cells: Wheatstone bridge
A basic load cell of any of these kinds consists of a complete strain gage bridge
If the strain gages reading strains ε2 and ε4 are placed in the load cell so as to read strains opposite in sign to strains ε1 and ε3 , the sensitivity and accuracy of the load cell improves.
This is accomplished by placing R1 and R3 in the direction of the applied force and R2 and R4 in the transverse direction
The strain gages 1, 2, 3, and 4 are arranged so as to eliminate the effect of the undesired stress components. From bridge theory, the output of the bridge may be expressed as:
ε0 = ‐ε1 + ε2 ‐ ε3 + ε4
Side View
Plan View
Connectionscheme
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Load cells
Thus ε0 = K ε1 where K = brdge multiplication factor(K = 2.6 if Poisson’s ration is 0.3).
Sensitivity of a load cell may be expressed in units of strain per unit load. Thus, it is directly proportional to the maximum stress used in the design of the cell and inversely proportional to its maximum load capacity.
E
stressdesignKK 10
E
K
loaddesign
stressdesign
loaddesignySensitivit 0
For a give design stress and design load, the optimum sensitivity will result from a maximum value of K and a minimum value of E
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Typical load cells
Load cells are used for measuring loads and reactions and other forces and can be classified into categories, depending on the type of loading.
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Load cells
A vast number of load cell types have developed over the years:
The first designs simply use a strain gauge to measure the direct stress which is introduced into a metal element when it is subjected to a tensile or compressive force
R1
R2
R3
R4
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Bending load cells
A bending beam type design uses strain gauges to monitor the stress in the sensing element when subjected to a bending force.
The strain gauges are bonded on the flat upper and lower sections of the cell at points of maximum strain. This load cell type is used for low capacities and performs with good linearity. Its disadvantage is that it must be load correctly to obtain consistent results.
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Bending load cells
Since the majority of the beam length serves only to increase the moment at the rigid clamp, various modifications of the simple beam are used to reduce the beam mass in the interest of maintaining a high natural frequency or to concentrate the strain at the strain gauge locations.
A review of beam bending characteristics reveals that the surface strain present in the beam surface linearly varies from the point offorce application to the clamp. This implies that the strain gauges will experience a strain gradient and provide an output equating to the average strain. Constant stress beam sections can be fabricated by tapering the edges of the beam such that the tapered edges projected intersect at the point of load application to the beam
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Bending load cells
Multiple cantilever structures produce a "multiple bending“ where tension and compression strain fields exist on the same surface of the beam.
Coupled dual‐beam load cell configurations conveniently produce equal and opposite axial loads within each of the beams in response to extraneous couples. Since the strain gauges can be wired to cancel the effects of axial loads, the result is a load cell structure largely insensitive to the point of load application. The sensitivity of the load cell to off‐axis loads is minimized.
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Bending Ring (Morehouse proving ring)
Both axial and bending occur within
the transduction zone of the sensor
characterizes ring‐style load cells.
The beauty of the proving ring with
strain gauges installed as shown is the
fact that all gauges of the Wheatstone
bridge ideally experience identical axial
strain, resulting in cancellation of axial
strain effects in the output of the bridge.
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Shear load cells
Strain gauge‐based load cell structures, configured to operate based upon the measurement of shear strain, provide high capacity and low compliance in a compact and low profile geometry.
It is a more efficient method of load determination as it is less dependent on the way and direction in which the force is applied to the load cell.
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Shear load cells
Strain gauges measuring shear are oriented at 45 degrees to the neutral axis in bending and are mounted to straddle the neutral axis. Bending stresses are, by definition, equal to zero at the neutral axis in bending. Although the strain gauge must possess some finite physical dimensions, by equally straddling the neutral axis in bending, half of each strain gauge will experience some bending strain while the other half will experience the same strain in the opposite direction thereby largely cancelling bending in the output of the sensor. Practically, the shear patterns cannot be positioned with absolute perfection and shear webs cannot be fabricated with absolute symmetry resulting in less than perfect cancellation of bending strains.
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Load cells errors
Excitation voltage
Higher excitation voltage increases the temperature gradient from the gages to the material
e.g. Interface cells operates at 10 VDC. Increasing the excitation voltage to 20 VDC would decrease sensitivity by 0.07%
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Load cells errors
Hysteresis
The difference between load cell output readings for the same applied load, one reading obtained by increasing the load from minimum load and the other by decreasing the load from maximum load.
This could be minimized by
“conditioning” the load cell.
Three cycles from zero to
130‐140% max load
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Load cells errors
Non linearity
The deviation of the increasing load cell calibration curve from either:
1) a straight line which passes through minimum load output and the load cell
output at 75% of the measuring range;
2) a straight line connecting the zero load
and the rated load output values;
3) the best straight line fitted to output
values by the least squares method,
through zero load output.
All measurements at a stable ambient
Temperature of 20°C or 68°F.
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Load cells errors
Creep
The change in load cell output occurring with time while under constant load (>90% of the load cell capacity ) and with all environmental conditions and other variables remaining constant.
Minimum Dead Load Output Return(MDLOR)
The difference in load cell output at
minimum dead load, measured
before and after a 30 minute load
application of at least 90% of the
cell's rated capacity
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Load cells errors
When we consider resolution, repeatability and reproducibility of load cell we need to consider the above performances in terms of the systems were the load cell are used.
The limiting factors are generally not associated with the load cell:
‐ proper application of the load cell
‐ loading systems and mechanical fixtures used to apply the loads
‐ electrical equipment used to measure the load cell output.
Difficult problems to solve:
‐ temperature variations
‐ forces such as air motion and building vibration
‐ inability of hydraulic systems to maintain a stable pressure
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Load cells errors
Repeatability is affected by any one of these factors:
‐ tightness of the mechanical connections of fixtures
‐ rigidity of the load frame or force application system
‐ repeatability of the hydraulic forcing system itself
‐ application of a dead weight load too quickly (impact)
‐ poor control of reading times introducing creep into data
‐ unstable electronics due to temperature drift, power line susceptibility, noise, etc.
Reproducibility?
The load cell is calibrated at one location and then used to measure forces at another location.
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Computer Vision System for High Precision Displacement Measurements
A number of applications prevents the use of traditional acquisition instruments and system.Application of fast or impulsive loads, large displacements tests, experimental activities possibly inducing partial or total collapse of the specimens are just some examples of tests for which normal transducers can not be used. The main reasons are:‐ limited reliability of the acquired signals (related to the high loading rate);‐ high risk of breaking transducers (high cost).
In these cases, particularly to avoid damages or loss of instrumentations, contact‐less transducers are an effective solution.
At Eucentre, we have developed a machine vision system: an optical acquisition system based on high definition cameras, retro‐reflective markers and infra‐red illumination.
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High definition digital cameras
Marker placed on the specimen
Digital camera
Markers identification
performed on acquired images
Pixel position
World coordinate (mm):
[150;50]px [240;80] mm
Measure positions of markers acquiring and analysing a series of digital images
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Hardware (Acquisition Unit)
Each acquisition unit is composed by:
• PC with UPS device in a ruggedized case
• X64 Xcelera CL-PX4 frame grabber, plugged into the PCI express 4x socket
• PT–40–04M60 (Pantera) high definition digital camera (Dalsa) with NIR filter and Illuminator
Camera resolution: 2352x1728 (8bpp) at 60Hz, scalable up to 2352x864 at 120Hz
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Hardware (Overall System)
• 10 ports KVM Switch for remote
management of acquisition units
• ISO Tech Signal generator for a triggered synchronized acquisition
• 3M® Reflective markers (rounded and flat shaped)
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Software (Acquisition Unit)
Multi layered software solution: EuVision (lower to higher abstraction level)• Dalsa Drivers (Sapera LT SDK) – interface to frame grabber• C++ / Assembly core analysis module – image compression / markers detection• OpenCV C++ higher level frame and signals filtering management• C++/CLI .NET front‐end (User Interface)• WCF / Remoting service ‐ listening for remote automation
• Performs the image acquisition• Detects and tracks blobs in the frame
• Converts pixel coordinates intoworld physical units
• Stores data in local or remote database
• Exposes measures to remote users
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Software (Overall System)
Remote Controller Application (EuRemote)
• Polls each connected unit state• Remotely sets acquisition and storing parameters• Remotely controls the acquisition (start/stop/pause)• Detects blobs identification issues and frames loss
.NET Remoting full duplex application, written in C#
• Optimized binary TCP/IP secure communication• Synchronized start/stop with < 8ms max phase error between acquisition units• Virtually unlimited number of stations connected
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Blob Detection
IR filter lenses make only the reflective markers visible in the scene when NIR lighting is on.
Calculation of the centroid for each blob, using colour intensity as weight parameter
Blob identification (recognition of a contiguous set of pixels after the application of a B/W threshold) in the scene
Precise up to
1/10 - 1/50 sub-pixel, using colour transitions
(depending on the threshold value and environmental lighting conditions)
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Blob Tracking (sequence)
A first image is acquired
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Blob Tracking (sequence)
A first image is acquired
The user can select and number the blobs to track
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Blob Tracking (sequence)
A first image is acquired
The user can select and number the blobs to track
Each new grabbed frame is analysed and measurements can be plotted during the acquisition
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Calibration (1 – parameters identification)Pin-hole camera model
Extrinsic parameters
Camera sensor and
lens distortion
(focus and lens non-
linearities)
Calibration result (calibration pattern is reconstructed in the image) Intrinsic parameters
(relative roto-translation
between the two coordinate systems –
camera & target)
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Calibration (2 – real world coordinates computation)
Knowing the roto-translation matrix allows for inverse computation of points lying on the calibration plane
On-line algorithm projects the optical ray of each blob center (in pixels coordinates) into the calibration
image plane (in physical length units [mm])
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System Synchronization
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Telepresence / remote visualization
• Blobs can be selected for on-line data transmission to the remote database
• Database allows concurrent transactional data access
• Remote applications can show live measurements during the test
3D geometry model
F.E.M. model with live displacements plotted
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SERIES‐POLYMAST Experiment
• 10 acquisition units connected• Following around 400 markers placed over the specimen• 60Hz sampling frequency• Cameras at a distance of 6-8 meters from the structure• Frame dimensions about 1.8 m x 2.0 m
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7700 7702 7704 7706 7708 7710 7712 7714
36.4
36.45
36.5
36.55
36.6
36.65
36.7
36.75
36.8
36.85
36.9
FoundationD
ispl
(m
m)
Found C3
Found C6Found C9 Detail of the displacement measured by
three different acquisition units.Notice the perfect phase of the signals.
500 1000 1500 2000 2500 3000 3500 4000 4500
-80
-60
-40
-20
0
20
40
60
80
Foundation
Dis
pl (
mm
)
Found C3
Found C6Found C9
Same plot in a wider range. The precision obtained (compared with traditional measurement devices) is near to 0.05 mm,
corresponding to a 1/10 – 1/20 sub-pixel in the frame
SERIES‐POLYMAST Experiment
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Movements of the measurement plane, like for example movements of the specimen towards the camera resulted in errors and distortions
The idea is to apply a simplified calibration pattern to the target plane and perform an on-line recalibration of the system during the tests
Out‐of‐plane error
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Calibration Plane
Errors
Actual Plane
Optical Centre
Calibration Origin
This error can be estimated directly dependent on the angle between the central optical ray (which connects the optical centre and the calibration origin) and the ray to the observed marker.
Out‐of‐plane error
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6 m
2 m
Reference
Two cameras at a distance between 6 and 8 meters from the calibration plane will measure the reference object displacements.This reference is then moved towards the cameras (and in general as orthogonally as possible to the calibration plane) and these movements are recorded by the application
Out‐of‐plane error estimation
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6 m
2 m
Reference
Two other cameras are placed and calibrated in order to follow the
out of plane movements above described (they need to be accurate as possible,
therefore they will be 2‐3 meters away)
Out‐of‐plane error estimation
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x
y
The two front cameras are calibrated on plane A
The reference is displaced along the x axis in order to cause a measurement error by effect of the out of plane offset
Out‐of‐plane error estimation
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x
y
The second couple of cameras is calibrated on a plane which is orthogonal to the previous one (plane B).They will therefore be extremely precise in the measurements of the out of plane movementBy combining the results on the two planes, the error made by the two frontal cameras will be estimated.
Out‐of‐plane error estimation
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mm
Out‐of‐plane error reduction
A simple error reduction can be performed by using the desired evolution of a target and comparing it to the actual displacement measured by the system. This can be the recording of a slow rigid movement of the test specimen or coming from an alternative acquisition device.
Slow building movement:
‐ 200 mm (±100mm)‐ Sinusoidal 0.03Hz‐ Sampled at 60Hz
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Out‐of‐plane error reduction
A central marker is used as the reference for the slow movement
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Out‐of‐plane error reduction
The algorithm considers and reduces the distance between the desiredmovement (main marker) and the measured evolution of any other marker.
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Out‐of‐plane error reduction
Plot of the evolution of the distance between a generic marker and the main marker. This distance should be as constant as possible in a slow rigid movement. The red line is the measured distance, the blue one is its corrected version.
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Out‐of‐plane error reduction(statistics)
Means and standard deviations of any marker compared to the main one (which histogram value is null by definition)
0,00
0,02
0,04
0,06
0,08
0,10
0,12
0,14
0,16
0,18
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43
Marker
Mean error (m
m)
before corrected
0,00
0,05
0,10
0,15
0,20
0,25
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43
Marker
Stan
dard
deviat
ion (m
m)
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EU‐Vision
The current implementation of the proposed machine vision system has shown a valuable precision when applied to planar measurements.The strong hypothesis of having each marker lying in the same plane used for the calibration for the entire acquisition, on the other side, is almost never valid for real applications.Different off‐line algorithms have been developed in order to overcome to the resulting measurement errors and currently a precise estimation of the effect of this issue is undergoing.
At the same time human and software resources have been allocated in light of a future stereoscopic vision mechanism to be combined to the actual architecture.
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• 8 acquisition units connected• Following around 250 markers placed over the specimen• 120Hz sampling frequency• Cameras at a distance of 6 meters from the structure• Frames wide around 1.80 x 1 meters
Example scheme and placing of the markers
Example of application
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Data Acquisition
National Instruments PXI
National Instruments
Analog‐Digital Converter
National Instruments
SCXI Multi‐Plexer Chassis
National Instruments
Signal Conditioner Boards
Connection Panels
Instruments
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System Performance
Acquisition speed up to 300 Ksample per second:
(the maximum sampling rate depends on the number of connected
instrument)
Sample type: 18 bit
Resolution 2x10‐17 V
Data Acquisition
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Architecture of an acquisition system
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Analog to Digital Conversion
Sampling QuantizationNumerical
coding
S(t) S(n) S*(n)
in
out
Ts
V0=000V1=001V2=010
:V7=111
V(t) V(n) V*(n) N(n)
Basics of Analog to DigitalConversion (A/D)
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Sampling: the delta distribution(pulse)
In the field of signal analysis some distributions are fundamental to describe some theoretical aspects.
The pulse or Dirac distribution, (t), can be viewed as the limit of a series of rectangular functions having increasing height and decreasing base in order to maintain a unitary area.
ttttd
h=1/d2h
d/2 d/4
4hy y y (t)
area=1 area=1area=1 area=1
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Sampling an analog signal
The operation of taking a sample of a continuous function y(t) at a time t1 is mathematically described as the product of y(t) with the pulse function (t‐t1).
t
(t -t1)
t1
y(t)
t
y(t1)(t -t1)
t1
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111
Sampling at a constant rate
Let us consider a sequence of infinite pulses spaced by a fixed time interval
t0 T 2T 3T 4T-T-2T
This distribution can be expressed by the following summation
i)iTt(
This distribution can be obtained as the limit of a periodic function f, withperiod T, containing all the harmonics of period T/k for k integer number ‐‐>
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Sampling in the time domain
The sampled signal, taken at the constant rate TS, in the continuous time, isdescribed by the product of y(t) and the sequence of delta distributions
t0 TC 2TC 3TC 4TC-TC-2TC
In the discrete time, it is described by a sequence of numbers yi = y(iTS)
i0 1 2 3 4-1-2
i
SSi
S iTtiTyiTtty )()()()(
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Sampling in the time domain
The basic question: “ Is the sampled signal equivalent to the analog signal ?”
It is possible to determine if some information is lost during the sampling process and, once the original signal y(t) has been sampled and transformed into a sequence y(n), is it possible to completely recover the original analog signal ?
To solve these problems we need to study the sampling process in the frequency domain through the Fourier transform.
The correct sampling rate for a signal can be chosen by making reference to the Nyquist or Shannon theorem.
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The sampling theorem(Nyquist or Shannon)
When digitizing an analog signal s(t) having a spectrum s(f) of limited bandwidth B (s(f)=0 for f>B), s(t) must be sampled, without loss of information, at a sampling frequency that is at least twice the signal highest frequency component B (SF 2B).
s(t)= sin(2ft), SF=f (Ts=1/f)
t
s(t) s(nTc)
samples constant component not present in s(t)
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Sampling
Examples of errors introduced by a SF too low
B) s(t)= sin(2ft), f<SF<2f (1/f>Ts>1/2f)
t
s(t) s(nTc)
Samples Low frequency oscillation thatdoes not exist in the original signal
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Sampling in the frequency domain
We start from the properties of the Fourier transform in the continuous time. The product in the time domain is equivalent to a convolution in the frequency domain.The sequence of pulses (Delta sequence) is a periodic signal of fundamental period Ts, containing all the harmonics with equal amplitude: then its Fourier transform is still a sequence of pulses equally spaced in the frequency domain of an amount SF=1/TS
f0 SF … 4SF…-2SF
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The result of sampling a waveform y(t) at a frequency SF is to replicate the FT of y =Y() around the multiple of S=2SF
k
Si
S )kωY(ω)iTδ(ty(t) k
F
TSSt
Y()y(t)
Sampling in the frequency domain
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Thus, if the sampling frequency is chosen higher than 2 times the maximumfrequency contained in signal, the spectra do not overlap when the samplingprocess replicate the original spectrum each s. Otherwise we can observe the foldover of the spectra (aliasing).
S 0 M
S 0 M
S/2yes
no
Sampling in the frequency domain
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Frequency analysis of a sampled signal
Once fixed the sampling frequency SF, the maximum frequency that can be represented is half of the sampling frequency, fN=SF/2=S/4 and it iscalled Nyquist frequency.
0 0 NN
2N-M M
For this reason, in the right example, the frequencies from N to M are notcorrectly represented.
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Example: let us consider 3 sinusoids at 1.2, 5.2 e 9.2 Hz all sampled at 4 Hz: they give exactly the same discrete signal that corresponds to the 1.2 Hz sinusoid.
Why?
Frequency foldover ‐ aliasing
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Aliasing: effect of spectra replication
As a matter of fact, the Fourier transform of the sinusoid at 1.2 Hz shows two pulses at +1.2 and at ‐1.2Hz, which are replicated symmetrically around 4 Hz due to the sampling process: they give pulses at 4k‐1.2 e 4k+1.2 Hz for k=1, 2, ..N
5.2 Hz = 4+1.2 Hz ‐‐> 4(k‐1)‐1.2 and 4(k+1)+1.2 Hz
9.2 Hz = 2x4+1.2 Hz ‐‐> 4(k‐2)‐1.2 e 4(k+2)+1.2 Hz
We thus find the same pulses in the frequency domain.
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Anti‐aliasing filtering
Once a SF has been chosen, we need to eliminate all frequency components higher than SF/2 before sampling the signal y(t) in order to avoid the aliasing phenomenon.
A/D converter
y(t) yi
Antialiasing filter
N
Simple first order antialiasing low pass active filter Note: the low pass
antialiasing filter is the only analog filter that cannot be substituted by a digital filter.
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Choice of the sampling frequency
1) Sampling theorem (SF>2fmax)
2) Time accuracy (if we want to measure events in time with an accuracy of t1, SF>1/t1 )
3) Processing algorithms (e.g. Numerical Differentiation – one of the most used algorithms for computing the derivative of a signal is the “two points central difference”, where the output is calculated as
This algorithm behaves like a derivative up to a frequency F=0.224 SF, then it behaves like a low pass filter.)
sT
kxkxky
2
)1()1()(
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Quantization
Quantization corresponds to the discretization in amplitude.
The number of levels that the ADC uses to represent the analog signal is the resolution. The amplitude of a single level is called quantization level. The higher the resolution (the smaller the quantization level), the larger the number of divisions the range is broken into, and therefore, the smaller the detectable voltage change. The figure shows a sine wave and its corresponding digital image as obtained by an ideal 3‐bit ADC.
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The quantization error
The quantization due to the A/D conversion introduces an approximationerror, that can be viewed as an additive noise (nQ)to the signal (y)
y^=y+nQ
The stochastic characteristics of the noise process can be easily determined:
1) the probability distribution is uniform from ‐Q/2 and Q/2 (the error can happen with equal probability in the quantization interval Q)
2) thus mean and variance are: mQ=0; Q2=Q2/12
3) it is a white noise
4) the noise is independent from the signal (it is not correlated)
5) the variance of the signal is increased by the quantization noise
y^2 = y
2 + Q2/12
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Quantization noise
Rounding Truncation
Probability density
mQ=0, Q2=Q2/12 mQ=-Q/2
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127
Quantization noise
The quantization level determines the accuracy of the A/D conversion.
The quantization level depends on the number of bits used by the A/D converter.
Example:•8 bit correspond to 28=256 different values.•Accuracy is 1/2560.4% of the whole analog range (usually from –5V to +5V or from –10V to +10V).
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Quantization and numerical coding
Range – Range refers to the minimum and maximum voltage levels that the ADC can quantize. Recent acquisition devices offer selectable ranges so that the device is configurable to handle a variety of voltage levels. With this flexibility, you can match the signal range to that of the ADC to take advantage of the available measurement resolution.
Code Width – The range, resolution, and gain available on an acquisition device determine the smallest detectable change in voltage. This change in voltage represents 1 least significant bit (LSB) of the digital value and is often called the code width. The ideal code width is found by dividing the voltage range by the gain times two raised to the order of bits in the resolution. For example, a 16‐bit acquisition device, has a selectable range of 0 to 10 or ‐10 to 10 V and selectable gain of 1, 2, 5, 10, 20, 50, or 100. With a voltage range of ‐10 to 10 V, and a gain of 20, the ideal code width is defined by the following equation:
V63,72201010
16
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Relative Accuracy – Relative accuracy is a measure in least significant bits of theworst‐case deviation from the ideal acquisition device transfer function, a straight line. Relative accuracy is determined by connecting a voltage at negative full scale, digitizing the voltage, increasing the voltage, and repeating the steps until the input range of the device has been covered. When the digitized points are plotted, the result will be an apparent straight line (left diagram). However, you can subtract actual straight‐line values from the digitized values and plot these resulting points, as shown in the right diagram. The maximum deviation from zero is the relative accuracy of the device.
Quantization and numerical coding
130
Continuous Waveform Acquisition
Data acquisition applications that do not have a predetermined number of samples, or that run for such lengths of time that a single buffer of data is too large to practically fit into memory may need to make use of continuous acquisition.
In a continuous acquisition, data is placed into a circular buffer by the hardware. Simultaneously, the software removes previously acquired data from the buffer, process and stores data on a permanent memory (disk). Typical processing operations include mathematical operations, screen display, and file I/O.
As long as the software removes data from the buffer at least as fast as the hardware provides it, the circular buffer never fills, and the operation may continue endlessly.
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131
The data buffer for double‐buffered input operations is configured as a circular buffer. In addition, the software logically divides the buffer into two equal halves. The coordination scheme is simple ‐ the software copies data from the circular buffer in sequential halves to a transfer buffer created by the user.
Double‐Buffered Input Operations
132
A problem occurs when an input device overwrites data before it has been transferred to the transfer buffer. The situation is presented in Figure
Another problem with continuous waveform acquisition is that the software fails to remove the data as fast as the hardware provides it. When this happens, an overrun condition occurs. This is due to the software loop that is retrieving thedata. If it becomes impossible to speed the code any further, the data acquisition will need to be slowed.
Problems with continuous acquisition
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Multiplexing
A common technique for measuring several signals with a single ADC is multiplexing. Signal conditioning hardware for analog signals often provides multiplexing for use with slowly changing signals.
The ADC samples one channel, switches to the next channel, samples it, switches to the next channel, and so on. Because the same ADC samples many channels instead of one, the effective sampling rate of each individual channel is inversely proportional to the number of channels sampled. For example, a converter sampling at 1 MS/s on 10 channels will effectively sample each individual channel at 100 KS/s
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Problems of multiplexing
1. Samples coming from different channels are never simultaneous
2. Even if singular signals present slow variations in time, the multiplexed signal may appear to be a high frequency oscillating signal (see Figure where a 40 channel multiplexed acquisition signal is represented)
3. The programmable amplifier before ADC must have a very fast response (settling time)
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135
136
Number of Channels – The number of analog channel inputs is specified for both single‐ended and differential inputs for devices with both input types.
Single‐ended inputs are all referenced to a common ground reference. These inputs are typically used when the input signals are high level (greater than 1 V), the leads from the signal source to the analog input hardware are short (less than 5 m), and all input signals share a common ground reference.
If the signals do not meet these criteria, you should use differential inputs. With differential inputs, each input has its own ground reference; noise errors are reduced because the common‐mode noise picked up by the leads is canceled out.
Analog inputs
Single ended (Potentiometer)
Floating source
(termocouple)
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137
We often describe the effect of the signal conditioning by the term transfer function. By this term we mean the effect of the signal transformation on the input signal. Thus, a simple voltage amplifier has a transfer function of some constant that, when multiplied by the input voltage, gives the output voltage.
It is possible to categorize signal conditioning into several general types:
• Signal level changes
• Linearization
• Conversions
• Filters and Impedance matching
• Loading
Signal conditioning
138
The simplest method of signal conditioning is to change the level of a signal. The most common example is the necessity to either amplify or attenuate a voltage level.
Generally, monitoring applications result in slowly varying signals where DC or low‐frequency response amplifiers can be employed. An important factor in the selection of an amplifier is the input impedance that the amplifier offers to the sensor (or any other element that serves as an input).
In process control, the signals are always representative of a process variable, and any loading effects obscure the correspondence between the measured signal and the variable value.
In some cases, such as accelerometers and optical detectors, the frequency response of the amplifier is very important.
Level change
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139
Often, signal conditioning is used to convert one type of electrical variation into another. In these cases, it is necessary to provide a circuit to convert this change either to a voltage or to a current signal. This is generally accomplished by bridgeswhen the fractional resistance change is small and/or by amplifiers whose gain varies with resistance.
Signal TransmissionAn important type of conversion is associated with the need of transmitting signals as 4‐20 mA current levels in wire. This gives rise to the need for converting resistance and voltage levels to an appropriate current level at the transmitting end and for converting the current back to voltage at the receiving end. Of course, current transmission is used because such a signal is independent of load variations other than accidental shunt conditions that may draw off some current. Thus, voltage‐to‐current and current‐to‐voltage converters are often required.
Conversions
140
Often, the dependence that exists between input and output of a sensor is nonlinear. Even those devices that are approximately linear may present problems when precise measurements of the variable are required. Historically, specialized analog circuits were devised to linearize signals. The modern approach to this problem is to provide the nonlinear signal as input to a computer and perform the linearization using software.
Virtually any nonlinearity can be handled in this manner and, with the speed of modern computers, in nearly real time.
Linearization
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Often, spurious signals of considerable strength are present in the testing environment, such as the 50 or 60‐Hz line frequency signals.
Motor start transients also may cause pulses and other unwanted signals in the process‐control loop. In many cases, it is necessary to use high‐pass, low‐pass, or notch filters to eliminate unwanted signals from the loop. Such filtering can be accomplished by passive filters using only resistors, capacitors, and inductors; or active filters, using operational amplifiers and feedback.
Impedance matching is an important element of signal conditioning when transducer internal impedance or line impedance can cause errors in measurement of a dynamic variable. Both active and passive networks are employed to provide such matching.
Filters and Impedance matching
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One of the most important concerns in analog signal conditioning is the loading of one circuit by another. Suppose the open circuit output of some element is a voltage, say Vx, when the element input is some variable of value x. Loading occurs when we do connect something, a load, across the output, and the output voltage of the element drops to some value, Vy < Vx.
Quantitatively, we can evaluate loading as follows. Thevenin's theorem tells us that the output terminals of any element can be defined as a voltage source in series with an output impedance.
Loading
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The element is modeled as a voltage VX and a resistance RX. Now suppose a load, RL, is connected across the output of the element as shown in the figure. RL could be the input resistance of an amplifier, for example. A current will flow and voltage will be dropped across RX. It is easy to calculate that the loaded output voltage will thus be given by
This equation shows how the effects of loading can be reduced. Clearly, the objective will be to make RL much larger than RX, that is, RL >> RX.
The ratio (Vx‐Vy)/Vx is called the loading error (or interconnection error).
Note: The input impedance of a good amplifier is of the order of tenths of MOhms and the output impedance of a transducer may vary from 100 ohms to tenths of kOhms.
xL
xxy RR
RVV 1
Loading
144
Scheme of a commerciallyavailable system
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145
Reducing Noise in Data Acquisition Systems
146
Current flow through one or more unintended paths, known as ground loops, creates measurement errors. Each ground has a unique voltage potential, which may differ from other grounds in a data acquisition system. Under general operating conditions, these potential differences, or common‐mode voltages, range from millivolts to tens of volts.
One way to minimize the large differences in ground potential is to use the same grounded AC outlet to power the computer, data acquisition system, and system under test.
Grounding problems
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However, even when all the data acquisition equipment operates from the same AC outlet, ground loops still occur.
In situations where a common‐mode voltage exceeds 10‐15 volts, users should consider employing isolated signal conditioning equipment. Generally, data acquisition systems that are isolated or that are floating electrically prevent ground loops.
Grounding problems
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When installing shielded leads, the shielding should never be grounded at both ends. Any potential difference ‐ causing current flow through the shield (with the capacitive proximity of the shield to the centre conductor) ‐ can result in a noisier connection. Grounding the leads at both ends also simultaneously couples other noise into the signal leads, which negates the advantage of using shielded leads.
Input leads made of twisted pairs often prevent noise as effectively as shielding. Twisted pairs are made by twisting two loose wires into a single spiral pair. The tighter the spiral, the more effective the twisted pair. Twisted pairs also improve most measurements taken in reverse proportion to the signal levels.
Input Leads
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In most cases, users can increase data accuracy by making differential voltage measurements (see Figure).
This is accomplished by attaching the channel input leads directly to the voltage point and the most appropriate reference point.
Differential connections work well because the noise on the high analog input lead closely approximates the noise on the low analog input lead. This noise voltage can be considerably higher than the signal that the user is attempting to measure.
Vm= V+ ‐ V‐
Differential Measurements
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One of the most common mistakes made when setting up a differential measurement is failing to establish a biasing path between their differential inputs. All differential measurement applications require a biasing path. Although specific applications may already have an established biasing path, others must have one established or the data will be invalid. Users can easily establish a biasing path by connecting a resistor (10 K Ohms to 1 M Ohms) from the low input line to the analog common line. In an application with multiple measurement points referenced to the same analog common line, users need only one connection to the data acquisition system's analog common line.
Differential Measurements
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Wiring configurations
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Wiring configurations
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Wiring configurations
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Many users may not consider averaging their data for fear of losing valuable information on signal variations. However, when the signal can be considered as steady, averaging provides more accurate data by reducing noise via the squareroot of a number of averaged data samples.
Data collected for dynamic signals should not be averaged because it tends to become distorted.
Before a user decides to average the data for their steady signal measurements, they should consider several important factors. Averaging generally eliminates only random noise; it cannot eliminate many types of system noise (e.g. noise that occurs with the same delay after a triggering event).
Averaging is useful only to the extent that the noise component of a signalaverages to zero. Noise in measurements decreases only as the square root of the number of measurements. Therefore, in certain applications, reducing the RMS noise to a single count by averaging would require far too many samples.
Averaging
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Analog and Digital Filtering
Some 50 (60), 100 (120), and 150 (180)‐Hz residual noise emitted from AC equipment is virtually impossible to eliminate only by an accurate wiring connections.
Depending on the frequency of the signal being measured, users can employ either low, or high‐pass, or notch filtering. Multiple filters provide greater attenuation. Sometimes a simple filtering approach at the signal source helps. For example, a small capacitor (range 0.001 µF to 0.1 µF) across a signal source removes much of the high‐frequency noise. This technique works well with strain gage outputs and other low‐level, low‐frequency sensors.
However, the best method to eliminate noise within the signal frequency range is through digital filters. They have numerous advantages with respect to analog filters:
1. they can be very sharp in eliminating undesired frequencies (notch).
2. they can be designed with zero phase shift (differently from analog filters that always present phase lead or lag).
3. most of them can operate in real‐time acquisition
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1. Oppenheim A.V. and Willsky A.V. “Signals and Systems”, Prentice‐Hall, 1983.
2. “Data acquisition fundamentals”, National Instruments Application Note 007, 2000
3. Schraff F., “Strategies for Increasing Measurement Accuracy: Reducing Noise in Data Acquisition Systems”, Sensors, 1996
4. Cerna M., Harvey A.F., “The fundamentals of FFT‐based signal analysis and measurement”, National Instruments Application Note 041, 2000
5. Benzoni G., “Experimental Mehods in Earthquake Engineering”, Notes of the MSc course at ROSE School (IUSS Pavia), 2010
References